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Opto-electronic and force compensated sensingelements have taken over from conventional optical systems, the most basicof which is the pointer and scale.Weights have always been based on multiples and sub-multiples ofnaturally occurring physical quantities such as a number of grains of wheat(hence the unit of the grain, one seven thousandth of a pound and the basis ofthe imperial system of weight). An artefact standard based on a naturalquantity (the weight of a cubic decimetre of water) is still used to maintainand disseminate the unit, nowadays on a global rather than a regional scale.The development of the balance as a measurement instrument has seenmodifications in the execution of the comparison technique rather than inthe technique itself. Current technology offers little improvement in terms ofresolution on the best knife-edge balances used during the eighteenth century[1].
For the last eighty years NMIs have been able to make measurements onkilogram weights to a resolution of a few micrograms [2]. Comparisons onsuch two pan balances were time-consuming and laborious and the limitedamount of data produced in turn limited the uncertainties that could beachieved. The recent automation of mass comparators, both in terms ofcollection of data and the exchange of weights, has allowed many more1CONTENTSTraceability oftraditional massmeasurementLow-massmeasurementLow-forcemeasurementReferencesThis section follows on from the introduction to mass given in section 2.4Fundamental Principles of Engineering NanometrologyCopyright Ó 2010 by Elsevier Inc.
All rights reserved.289290C H A P T ER 1 0: Mass and force measurementcomparisons of standards and unknowns to be made. The increase in datacollected allows statistical analysis and this, rather than an absoluteimprovement in the overall resolution or accuracy of the instrument, has ledto an improvement in the uncertainty with which the kilogram can bemonitored and disseminated.The current state of the art in mass measurement allows the comparisonof kilogram weights with a repeatability approaching 1 mg on mass comparators, which can reliably be used on a daily basis.
With this frequency ofcalibration, the stability of the standard weight used as a reference becomessignificant not only at the working standards level but also for nationalstandards and for the International Prototype Kilogram itself. For this reasonthere is interest both in the absolute stability of the unit of the kilogram andin the way it is defined and disseminated.10.1.1 Manufacture of the Kilogram weightand the original copiesAfter many attempts in France, Johnson Matthey of London made a successfulcasting of a 90 % platinum 10 % iridium alloy mass standard in 1879. Threecylindrical pieces were delivered to St-Claire Deville metallurgists in Francewhere they were hammered in a press to eliminate voids, rough machined andpolished and finally adjusted against the kilogram des archives [3].
One ofthese kilograms was designated K and became the International PrototypeKilogram. Forty further kilogram weights were produced using the sametechniques and delivered in 1884. Twenty of these were allocated to thesignatories of the convention of the metre as national standards.The International Prototype Kilogram (commonly known as the (International) Kilogram or just K) is a cylinder of approximate dimensions 39 mmdiameter by 39 mm height [4] (see Figure 2.4). The design of the artefactminimizes its surface area while making it easy to handle and machine (asphere would give the minimum surface area but presents difficulties inmanufacture and use).
Platinum-iridium was chosen as the material for thekilogram for a number of reasons. Its high density (approximately 21.5 kg$m3)means that the artefact has a small surface area and, therefore, the potential forsurface contamination is minimized. The relatively inert nature of the materialalso minimizes surface contamination and enhances the mass stability of theartefact. The high density of the material also means that it displaces a smalleramount of air than a kilogram of less dense material (stainless steel or brass forexample). The weight-in-air of the kilogram (or any mass standard) depends onthe density of the air in which it is weighed because the air (or any fluid in whichit is weighed) exerts a buoyancy effect proportional to the volume of the artefact.Traceability of traditional mass measurementMinimizing the volume of the weight minimizes the effect of changing airdensity on the weight of the artefact. Platinum and its alloys are reasonably easyto machine [5], enabling a good surface finish to be achieved on the artefact,again reducing the effect of surface contamination.
The addition of 10 %iridium to the platinum greatly increases its hardness and so reduces wear.10.1.2 Surface texture of mass standardsThe surface texture of the kilogram standards has a major effect on theirstability. Early copies of the International Prototype (and the Kilogram itself)were finished by hand polishing using gradually finer polishing grains,concluding finally by polishing with a grain diameter of 0.25 mm [6]. Morerecent copies (since 1960) have been diamond-turned, producing a visiblybetter finish on the surface. Measurements using coherence scanninginterferometry have shown typical surface roughness (Ra) values of 65 nm to85 nm for hand-polished weights, compared with 10 nm to 15 nm achievedby diamond turning [7].10.1.3 Dissemination of the kilogramThe BIPM is responsible for the dissemination of the unit of mass worldwide.Dissemination is achieved via official copies of the International PrototypeKilogram, known as national prototypes, held by all countries that aresignatories to the Metre Convention.
These are periodically compared, at theBIPM, with the International Prototype. The official copies of the kilogramare, like the original, made of platinum-iridium alloy and the final machiningand adjustment is done at BIPM. At present there are approximately ninetyofficial copies of the kilogram.Periodic verification of the national kilogram copies takes place approximately every ten years [8]. Each time the national copies are returned to theBIPM they are cleaned and washed by a process known as nettoyage-lavage[9], which theoretically returns them to a reference value. All kilograms,including the International Prototype, are subject to nettoyage-lavage prior tothe periodic verification exercise.
The BIPM justify the use of this cleaningprocess because of the wide spread in the contamination levels of thereturning national prototypes and the need to return K to its reference value.Surface contamination varies between national copies and ranges from thosewhich are not used at all (some are returned to the BIPM with the seal on thecontainer still intact from the last verification) to those that are used ona regular basis and have collected many tens of micrograms worth of accretedmaterial on their surfaces.291292C H A P T ER 1 0: Mass and force measurement10.1.4 Post nettoyage-lavage stabilityAlthough the gravimetric effects of the nettoyage-lavage process have beenstudied by various NMIs [8,10,11] and the (variable) reproducibility of themethod is documented, no work has been done to link the actual effect onthe surface of the weight (measured by a reliable surface analysis technique) with either the mechanical cleaning method or the observed weightloss.
Furthermore, while the BIPM has made studies of the mass gain overthe first three months after cleaning based on the behaviour of all thenational prototypes, the return of the prototypes to their NMIs after thisperiod means no longer-term studies have been made. Only an NMI withat least three other platinum-iridium kilograms, against which the stabilityof the national prototype could be monitored, would be able to carry outsuch work and even so the stability of the other three kilograms wouldaffect the results.
Due to the lack of data on the stability of nationalstandards after returning from BIPM (approximately three to four monthsafter cleaning and so relatively unstable) a wide variety of algorithms areused to predict the longer-term mass gain of the kilogram standards. Somealgorithms are expressed as a function of time; for example, NPL has usedthe following expression to predict the value of kilogram 18 after cleaningat the BIPMMass18 ¼ 1 kg þ DV þ 0:356097t0:511678 mg(10.1)where DV is the measured difference from nominal in micrograms directly aftercleaning (as measured by the BIPM) and t is the time after cleaning in days.The most commonly used algorithm is that the national standard has thevalue assigned on leaving BIPM (approximately three months after cleaning)plus 1 mg per year. Some NMIs modify this by using a 0.22 mg per month gainfor the first two years.
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